CAREER: Demystifying Deep Machine Learning Models using Convex Optimization for Reliable AI

该项目开发了深度神经网络的理论框架，这是一种机器学习模型，在图像和语音识别、机器人学和自动化等一系列应用中取得了巨大成功。尽管这些模式取得了成功，但在理解它们如何作出决策或如何使它们更有效率、更稳健和更可靠方面，仍有许多悬而未决的问题。此外，深度神经网络的内部工作缺乏透明度，这可能会使人们很难相信他们的输出并解释他们的结果。通过开发一个理论框架来研究和训练这些模型，凸性是最优化理论中一个研究得很好的数学概念，该项目旨在提高它们的可靠性和可解释性，最终导致更高效和更值得信赖的人工智能系统。该项目同样寻求通过实现安全和有效的人工智能应用来教育下一代研究人员，并造福社会。该技术方法基于一种新的凸分析框架来研究、训练和验证非凸模型，包括深度神经网络。通过利用非凸训练损失中隐藏的凸优化场景，该项目开发了一个理论基础，应该揭开这些模型的最优化和泛化特性的神秘面纱。通过应用信号处理、压缩传感和凸优化的技术，该项目寻求统一来自不同领域的想法和方法，以促进非凸模型的技术水平。这将促进我们对深度神经网络基本行为的理解，并减轻与使用它们相关的挑战。此外，本项目还将通过凸优化的视角来考察这些模型在实际应用中的可解释性、可验证性和稳健性。神经网络的多样化应用可以吸引不同背景的研究生，并有助于将现代深度学习主题整合到信号处理课程中。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project develops a theoretical framework for deep neural networks, a type of machine learning model that has had tremendous success in a range of applications including image and speech recognition, robotics, and automation. Although these models have been successful, there remain significant open questions in the understanding of how they make decisions or how they can be made more efficient, robust and reliable. Additionally, there is a lack of transparency in the inner workings of deep neural networks, which can make it difficult to trust their output and interpret their results. By developing a theoretical framework to study and train these models based on convexity, which is a well-studied mathematical concept in optimization theory, this project aims to improve their reliability and interpretability, ultimately leading to more efficient and trustworthy artificial intelligence systems. This project likewise seeks to educate the next generation of researchers, and benefit society by enabling safe and effective applications of artificial intelligence.The technical approach is based on a novel convex analytic framework to study, train, and validate non-convex models, including deep neural networks. By leveraging the hidden convex optimization landscape in non-convex training losses, this project develops a theoretical foundation that should demystify the optimization and generalization properties of these models. By applying techniques from signal processing, compressed sensing and convex optimization, the project seeks to unify ideas and methods from diverse fields in order to advance the state of the art in non-convex models. This will advance our understanding of the fundamental behavior of deep neural networks and mitigate challenges associated with their use. In addition, this project will investigate the interpretability, verifiability and robustness of these models through the lens of convex optimization in practical applications. The diverse applications of neural networks can attract graduate students with diverse backgrounds and contribute to the integration of modern deep learning topics in signal processing courses.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.